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Math Help - Why do I keep getting this wrong?

  1. #1
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    Why do I keep getting this wrong?

    The problem


    3x-(1+2x)=6 Please pretend the parenthesis are aboslute value bars

    my solution

    -(1+2x)=-6+3x divide both sides by -1

    (1+2x)=6-3x


    1+2x=6-3x or 1+2x=-6-3x

    x= 1 or x=7, but only seven is valid in the original equation. Why?










    Thank you in advance!
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  2. #2
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    Quote Originally Posted by Coach View Post
    The problem


    3x-(1+2x)=6 Please pretend the parenthesis are aboslute value bars

    my solution

    -(1+2x)=-6+3x divide both sides by -1

    (1+2x)=6-3x


    1+2x=6-3x or 1+2x=-6-3x

    x= 1 or x=7, but only seven is valid in the original equation. Why?

    Thank you in advance!
    |1 + 2x| = 3x - 6.

    Note that:
    1. |1 + 2x| = 1 + 2x when 1 + 2x > 0 => x > -1/2.
    2. |1 + 2x| = -(1 + 2x) = -1 - 2x when 1 + 2x < 0 => x < -1/2.

    1. 1 + 2x = 3x - 6 AND x > -1/2 => x = 7 AND x > -1/2 => x = 7.

    2. -1 - 2x = 3x - 6 AND x < -1/2 => x = 1 AND x < -1/2 => no solution.

    So x = 7 is the only solution.
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